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Costas Loop
A Costas loop is a phase-locked loop (PLL) based circuit which is used for carrier frequency recovery from suppressed-carrier modulation signals (e.g. double-sideband suppressed carrier signals) and phase modulation signals (e.g. BPSK, QPSK). It was invented by John P. Costas at General Electric in the 1950s. Its invention was described as having had "a profound effect on modern digital communications". The primary application of Costas loops is in wireless receivers. Its advantage over other PLL-based detectors is that at small deviations the Costas loop error voltage is \sin(2(\theta_i-\theta_f)) as compared to \sin(\theta_i-\theta_f). This translates to double the sensitivity and also makes the Costas loop uniquely suited for tracking Doppler-shifted carriers, especially in OFDM and GPS receivers. Classical implementation In the classical implementation of a Costas loop, a local voltage-controlled oscillator (VCO) provides quadrature outputs, one to each of two phase dete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase-locked Loop
A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a variable frequency oscillator and a phase detector in a feedback loop. The oscillator's frequency and phase are controlled proportionally by an applied voltage, hence the term voltage-controlled oscillator (VCO). The oscillator generates a periodic signal of a specific frequency, and the phase detector compares the phase of that signal with the phase of the input periodic signal, to adjust the oscillator to keep the phases matched. Keeping the input and output phase in lockstep also implies keeping the input and output frequencies the same. Consequently, in addition to synchronizing signals, a phase-locked loop can track an input frequency, or it can generate a frequency that is a multiple of the input frequency. These properties are use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal (information Theory)
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' includes audio, video, speech, image, sonar, and radar as examples of signal. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information. In nature, signals can be actions done by an organism to alert other organisms, ranging from the release of plant chemicals to warn nearby plants of a predator, to sounds or motions made by animals to alert other animals of food. Signaling occurs in all organisms even at cellular levels, with cell signaling. Signaling theory, in evolutionary biology, proposes that a substantial driver for evolution is the ability of animals to communicate with each other by developing ways of signaling. In human engineering, signals are typi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Costas Loop After Sync
Kostas or Costas ( el, Κώστας) is a Greek given name and surname. As a given name it is the hypocorism for Konstantinos (Constantine (name), Constantine). Given name * Costas Andreou, Greek musician * Kostas Antetokounmpo (born 1997), a Greek basketball player * Costas Azariadis (born 1943), Greek economist * Kostas Biris (1899–1980), Greek architect * Costas Georgiou (1951–1976), Greek Cypriot mercenary * Kostas Lazarides (born 1949), aka Kostas (songwriter), Greek-American country music songwriter * Costas Mandylor (born 1965), Greek Australian actor * Kostas Papanikolaou (born 1990), Greek basketball player * Costas Rigas (born 1944), Greek basketball player * Costas Simitis (born 1936), former Prime Minister of Greece * Kostas Hatzichristos (1921–2001), Greek actor * Kostas Karamanlis (born 1956), former Prime Minister of Greece * Kostas Koufogiorgos (born 1972), Greek-German cartoonist Surname * Bob Costas (born 1952), American sportscaster and talk show host * John ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Costas Loop Before Sync
Kostas or Costas ( el, Κώστας) is a Greek given name and surname. As a given name it is the hypocorism for Konstantinos (Constantine). Given name * Costas Andreou, Greek musician * Kostas Antetokounmpo (born 1997), a Greek basketball player * Costas Azariadis (born 1943), Greek economist * Kostas Biris (1899–1980), Greek architect * Costas Georgiou (1951–1976), Greek Cypriot mercenary * Kostas Lazarides (born 1949), aka Kostas (songwriter), Greek-American country music songwriter * Costas Mandylor (born 1965), Greek Australian actor * Kostas Papanikolaou (born 1990), Greek basketball player * Costas Rigas (born 1944), Greek basketball player * Costas Simitis (born 1936), former Prime Minister of Greece * Kostas Hatzichristos (1921–2001), Greek actor * Kostas Karamanlis (born 1956), former Prime Minister of Greece * Kostas Koufogiorgos (born 1972), Greek-German cartoonist Surname * Bob Costas (born 1952), American sportscaster and talk show host * John P. Costas (enginee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase-locked Loop Ranges
The terms hold-in range, pull-in range (acquisition range), and lock-in range are widely used by engineers for the concepts of frequency deviation ranges within which phase-locked loop-based circuits can achieve lock under various additional conditions. History In the classic books on phase-locked loop A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a ...s, published in 1966, such concepts as hold-in, pull-in, lock-in, and other frequency ranges for which PLL can achieve lock, were introduced. They are widely used nowadays (see, e.g. contemporary engineering literature and other publications). Usually in engineering literature only non-strict definitions are given for these concepts. Many years of using definitions based on the above concepts has led to the advice given in a handbook o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Krylov–Bogoliubov Averaging Method
The Krylov–Bogolyubov averaging method (Krylov–Bogolyubov method of averaging) is a mathematical method for approximate analysis of oscillating processes in non-linear mechanics. The method is based on the averaging principle when the exact differential equation of the motion is replaced by its averaged version. The method is named after Nikolay Krylov and Nikolay Bogoliubov. Various averaging schemes for studying problems of celestial mechanics were used since works of Gauss, Fatou, Delone, Hill. The importance of the contribution of Krylov and Bogoliubov is that they developed a general averaging approach and proved that the solution of the averaged system approximates the exact dynamics. Background Krylov–Bogoliubov averaging can be used to approximate oscillatory problems when a classical perturbation expansion fails. That is singular perturbation problems of oscillatory type, for example Einstein's correction to the perihelion precession of Mercury Tests of general ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autonomous System (mathematics)
In mathematics, an autonomous system or autonomous differential equation is a system of ordinary differential equations which does not explicitly depend on the independent variable. When the variable is time, they are also called time-invariant systems. Many laws in physics, where the independent variable is usually assumed to be time, are expressed as autonomous systems because it is assumed the laws of nature which hold now are identical to those for any point in the past or future. Definition An autonomous system is a system of ordinary differential equations of the form \fracx(t)=f(x(t)) where takes values in -dimensional Euclidean space; is often interpreted as time. It is distinguished from systems of differential equations of the form \fracx(t)=g(x(t),t) in which the law governing the evolution of the system does not depend solely on the system's current state but also the parameter , again often interpreted as time; such systems are by definition not autonomous. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Detector Characteristic
A phase detector characteristic is a function of phase difference describing the output of the phase detector. For the analysis of Phase detector it is usually considered the models of PD in signal (time) domain and phase-frequency domain. In this case for constructing of an adequate nonlinear mathematical model of PD in phase-frequency domain it is necessary to find the characteristic of phase detector. The inputs of PD are high-frequency signals and the output contains a low-frequency error correction signal, corresponding to a phase difference of input signals. For the suppression of high-frequency component of the output of PD (if such component exists) a low-pass filter is applied. The characteristic of PD is the dependence of the signal at the output of PD (in the phase-frequency domain) on the difference of phases at the input of PD. This characteristic of PD depends on the realization of PD and the types of waveforms of signals. Consideration of PD characteristic allows to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PLL Trainsient Process Phase Domain
A phase-locked loop or phase lock loop (PLL) is a control system that generates an output signal whose phase is related to the phase of an input signal. There are several different types; the simplest is an electronic circuit consisting of a variable frequency oscillator and a phase detector in a feedback loop. The oscillator's frequency and phase are controlled proportionally by an applied voltage, hence the term voltage-controlled oscillator (VCO). The oscillator generates a periodic signal of a specific frequency, and the phase detector compares the phase of that signal with the phase of the input periodic signal, to adjust the oscillator to keep the phases matched. Keeping the input and output phase in lockstep also implies keeping the input and output frequencies the same. Consequently, in addition to synchronizing signals, a phase-locked loop can track an input frequency, or it can generate a frequency that is a multiple of the input frequency. These properties are used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-autonomous System (mathematics)
In mathematics, an autonomous system is a dynamic equation on a smooth manifold. A non-autonomous system is a dynamic equation on a smooth fiber bundle Q\to \mathbb R over \mathbb R. For instance, this is the case of non-autonomous mechanics. An ''r''-order differential equation on a fiber bundle Q\to \mathbb R is represented by a closed subbundle of a jet bundle J^rQ of Q\to \mathbb R. A dynamic equation on Q\to \mathbb R is a differential equation which is algebraically solved for a higher-order derivatives. In particular, a first-order dynamic equation on a fiber bundle Q\to \mathbb R is a kernel of the covariant differential of some connection \Gamma on Q\to \mathbb R. Given bundle coordinates (t,q^i) on Q and the adapted coordinates (t,q^i,q^i_t) on a first-order jet manifold J^1Q, a first-order dynamic equation reads : q^i_t=\Gamma (t,q^i). For instance, this is the case of Hamiltonian non-autonomous mechanics. A second-order dynamic equation : q^i_=\xi^i(t,q^j,q^j_t) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Filter
Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using LTI ("linear time-invariant") system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Real-time implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions. An analog electronic circuit consisting only of linear components (resistors, capacitors, inductors, and linear amplifiers) will necessarily fall in this category, as will comparable mechanical systems or digital signal processing systems containing only linear elements. Since linear time-invariant filters can be completely characterized by their response to sinusoids of different frequencies (their frequency response), they are so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
